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Seminar by G. G. Amosov and A. V. Utkin "Current Problems in the Theory of One-Parameter Semigroups"
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Seminar 10. Several Straightforward Results on Quantum Dynamical Semigroups, Part 1 V. I. Yashin |
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Abstract: The dynamics of finite-dimensional open quantum systems in the Markovian approximation is described by completely positive one-parameter semigroups on the space of finite-dimensional density matrices. The generators of such semigroups are given by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) form. Despite the analytic simplicity of these semigroups and their long history of study, many of their properties remain poorly understood. In this talk, I will discuss several (time permitting) recent and intriguing results by Frederik vom Ende, which are elementary in their formulation and proof. List of related papers: 1. Purification Theorem: A result showing that purifying Lindbladian dynamics to a unitary dynamics requires an infinite-dimensional environment. https://arxiv.org/abs/2211.08351 https://arxiv.org/pdf/2306.03667 2. A Refinement of the GKSL Theorem: A certain strengthening of the standard GKSL representation. https://arxiv.org/abs/2310.04037 https://arxiv.org/abs/2401.14344 3. On Spectral Properties of Generators in Completely Positive Dynamics: Investigations into the spectrum of generators for completely positive dynamics. https://arxiv.org/abs/2505.24467 https://arxiv.org/abs/2506.02145 https://arxiv.org/abs/2510.19657 |
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